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b/Homework_5.1/2D/README-2D @@ -0,0 +1,33 @@ + 2D geometry and matches + ----------------------- + +Files: + ###.corners Affine multiscale Harris corners. ASCII x y coordinates, one per line + ###.lines Line segments. ASCII x0 y0 x1 y1, one per line + + nview-corners Corner matches + nview-lines Line matches + + The image coordinate frame (to which files ###.corners and ###.lines refer) + is as follows: the top-left image pixel has coordinates (0,0), first axis + aims to the right, second axis aims down. + + +Match format: (e.g. nview-corners) + + Each row of the file corresponds to one 3d feature (these features are in files + p3d and l3d) and contains #images integers (one per view) indicating + which corner is the image of the 3D point in the associated + view. Views in which the point does not appear are marked with an asterisk. + + For example the line + 134 * 132 131 * * * * * * * * + indicates that this 3D point : + corresponds to corner 134 in view 1, + has no match in view 2, + corresponds to corner 132 in view 3, + corresponds to corner 131 in view 4, + and has no matches through the rest of the sequence. + + Note that indices of points and lines start from zero, and are indices into + the appropriate ".corners" or ".lines" files. \ No newline at end of file diff --git a/Homework_5.1/2D/nview-corners b/Homework_5.1/2D/nview-corners new file mode 100644 index 0000000..5955705 --- /dev/null +++ b/Homework_5.1/2D/nview-corners @@ -0,0 +1,575 @@ + 0 0 * + 1 1 * + 2 2 * + 3 3 * + 4 * 0 + 5 4 * + 6 * 1 + 7 * 2 + 8 * 3 + 9 * 4 + 10 * 5 + 11 5 * + 12 * 6 + 13 * 7 + 14 * 8 + 15 * 9 + 16 6 * + 17 * 10 + 18 7 * + 19 8 * + 20 * 11 + 21 * 12 + 22 * 13 + 23 * 14 + 24 9 * + 25 * 15 + 26 10 * + 27 11 * + 28 * 16 + 29 12 * + 30 * 17 + 31 13 * + 32 14 * 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b/Homework_5.1/3D/README-3D @@ -0,0 +1,8 @@ + 3D reconstruction + ----------------- + +Files: + ###.P 3x4 camera projection matrix, one per image. + p3d 3D points. ASCII x y z coordinates, one per line + l3d 3D line segments. 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3.3407139e-02 + 4.3520343e+00 -6.0413290e-01 2.6309313e+00 + 5.3667670e+00 -2.8479408e-01 3.9365875e-02 + 3.1923853e+00 -6.2141059e+00 5.1624334e+00 + 1.4225223e+00 1.0465825e+00 -7.0223162e-02 diff --git a/Homework_5.1/camera.py b/Homework_5.1/camera.py new file mode 100644 index 0000000..1abf519 --- /dev/null +++ b/Homework_5.1/camera.py @@ -0,0 +1,74 @@ +from numpy import * +from scipy import linalg + + +class Camera(object): + """ Class for representing pin-hole cameras. """ + + def __init__(self,P): + """ Initialize P = K[R|t] camera model. """ + self.P = P + self.K = None # calibration matrix + self.R = None # rotation + self.t = None # translation + self.c = None # camera center + + + def project(self,X): + """ Project points in X (4*n array) and normalize coordinates. """ + + x = dot(self.P,X) + for i in range(3): + x[i] /= x[2] + return x + + + def factor(self): + """ Factorize the camera matrix into K,R,t as P = K[R|t]. """ + + # factor first 3*3 part + K,R = linalg.rq(self.P[:,:3]) + + # make diagonal of K positive + T = diag(sign(diag(K))) + if linalg.det(T) < 0: + T[1,1] *= -1 + + self.K = dot(K,T) + self.R = dot(T,R) # T is its own inverse + self.t = dot(linalg.inv(self.K),self.P[:,3]) + + return self.K, self.R, self.t + + + def center(self): + """ Compute and return the camera center. """ + + if self.c is not None: + return self.c + else: + # compute c by factoring + self.factor() + self.c = -dot(self.R.T,self.t) + return self.c + + + +# helper functions + +def rotation_matrix(a): + """ Creates a 3D rotation matrix for rotation + around the axis of the vector a. """ + R = eye(4) + R[:3,:3] = linalg.expm([[0,-a[2],a[1]],[a[2],0,-a[0]],[-a[1],a[0],0]]) + return R + + +def rq(A): + from scipy.linalg import qr + + Q,R = qr(flipud(A).T) + R = flipud(R.T) + Q = Q.T + + return R[:,::-1],Q[::-1,:] diff --git a/Homework_5.1/figure_1.png b/Homework_5.1/figure_1.png new file mode 100644 index 0000000..ee64de4 Binary files /dev/null and b/Homework_5.1/figure_1.png differ diff --git a/Homework_5.1/figure_2.png b/Homework_5.1/figure_2.png new file mode 100644 index 0000000..94be026 Binary files /dev/null and b/Homework_5.1/figure_2.png differ diff --git a/Homework_5.1/func_epipolar.py b/Homework_5.1/func_epipolar.py new file mode 100644 index 0000000..de405ee --- /dev/null +++ b/Homework_5.1/func_epipolar.py @@ -0,0 +1,50 @@ +import numpy +import pylab + +# Compute fundamental matrix +# x1, x2 = corresponding points (3*n arrays) +def compute_fundamental(x1,x2): + + n = x1.shape[1] + + A = numpy.zeros((n,9)) + for i in range(n): + A[i] = [x1[0,i]*x2[0,i], x1[0,i]*x2[1,i], x1[0,i]*x2[2,i], + x1[1,i]*x2[0,i], x1[1,i]*x2[1,i], x1[1,i]*x2[2,i], + x1[2,i]*x2[0,i], x1[2,i]*x2[1,i], x1[2,i]*x2[2,i] ] + + # compute linear least square solution + U,S,V = numpy.linalg.svd(A) + F = V[-1].reshape(3,3) + + # constrain F + # make rank 2 by zeroing out last singular value + U,S,V = numpy.linalg.svd(F) + S[2] = 0 + F = numpy.dot(U,numpy.dot(numpy.diag(S),V)) + + return F/F[2,2] + +# Compute epipole by using fundamental matrix F +def compute_epipole(F): + + U,S,V = numpy.linalg.svd(F) + e = V[-1] + return e/e[2] + +# Plot epipolar line on the original image +def plot_epipolar_line(im,F,x,epipole=None,show_epipole=True): + + m,n = im.shape[:2] + line = numpy.dot(F,x) + + t = numpy.linspace(0,n,100) + lt = numpy.array([(line[2]+line[0]*tt)/(-line[1]) for tt in t]) + + ndx = (lt>=0) & (lt=0) & (corr[:,1]>=0) + + +x1 = points2D[0][:,corr[ndx,0]] +x1 = numpy.vstack( (x1,numpy.ones(x1.shape[1])) ) + +x2 = points2D[1][:,corr[ndx,1]] +x2 = numpy.vstack( (x2,numpy.ones(x2.shape[1])) ) + +# Compute fundamental matrix +F = func_epipolar.compute_fundamental(x1,x2) + +# Compute epipole +e = func_epipolar.compute_epipole(F) + +# Show image1 +pylab.figure() +pylab.imshow(im1) +for i in range(5): + func_epipolar.plot_epipolar_line(im1,F,x2[:,i],e,False) +pylab.axis('off') + +# Show image2 +pylab.figure() +pylab.imshow(im2) +for i in range(5): + pylab.plot(x2[0,i],x2[1,i],'o') +pylab.axis('off') + +pylab.show() \ No newline at end of file diff --git a/Homework_5.1/stereo/left.jpg b/Homework_5.1/stereo/left.jpg new file mode 100644 index 0000000..1e8a972 Binary files /dev/null and b/Homework_5.1/stereo/left.jpg differ diff --git a/Homework_5.1/stereo/right.jpg b/Homework_5.1/stereo/right.jpg new file mode 100644 index 0000000..9d522ac Binary files /dev/null and b/Homework_5.1/stereo/right.jpg differ diff --git a/Homework_5.2/2D/001.P b/Homework_5.2/2D/001.P new file mode 100644 index 0000000..42545f8 --- /dev/null +++ b/Homework_5.2/2D/001.P @@ 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5.6000358e+01 + 2.0404645e+02 1.8977022e+01 1.9023612e+02 1.1749497e+01 + 1.0117653e+03 4.7972048e+01 1.0133258e+03 2.2028618e+01 + 9.7779389e+02 6.9896574e+00 9.7664638e+02 2.2978784e+01 + 9.6862884e+02 4.0010122e+01 9.7318252e+02 7.0223823e+01 + 9.7431758e+02 7.1999306e+01 9.7740747e+02 1.2799738e+02 + 9.7308533e+02 1.3298660e+02 9.7925668e+02 1.7690205e+02 + 1.0200065e+03 1.7978499e+02 9.8200764e+02 1.8242787e+02 + 5.2697869e+02 9.3804177e+01 5.2446444e+02 3.0048685e+01 + 5.2978213e+02 1.5199042e+02 5.3036459e+02 1.1398591e+02 + 5.6797216e+02 2.0549706e+02 5.5097882e+02 2.0805532e+02 + 3.8744978e+02 3.0000182e+00 3.8748180e+02 2.1000070e+01 + 3.4500629e+02 3.7999992e+01 3.4504655e+02 1.4999941e+01 diff --git a/Homework_5.2/2D/README-2D b/Homework_5.2/2D/README-2D new file mode 100644 index 0000000..e868668 --- /dev/null +++ b/Homework_5.2/2D/README-2D @@ -0,0 +1,33 @@ + 2D geometry and matches + ----------------------- + +Files: + ###.corners Affine multiscale Harris corners. ASCII x y coordinates, one per line + ###.lines Line segments. ASCII x0 y0 x1 y1, one per line + + nview-corners Corner matches + nview-lines Line matches + + The image coordinate frame (to which files ###.corners and ###.lines refer) + is as follows: the top-left image pixel has coordinates (0,0), first axis + aims to the right, second axis aims down. + + +Match format: (e.g. nview-corners) + + Each row of the file corresponds to one 3d feature (these features are in files + p3d and l3d) and contains #images integers (one per view) indicating + which corner is the image of the 3D point in the associated + view. Views in which the point does not appear are marked with an asterisk. + + For example the line + 134 * 132 131 * * * * * * * * + indicates that this 3D point : + corresponds to corner 134 in view 1, + has no match in view 2, + corresponds to corner 132 in view 3, + corresponds to corner 131 in view 4, + and has no matches through the rest of the sequence. + + Note that indices of points and lines start from zero, and are indices into + the appropriate ".corners" or ".lines" files. \ No newline at end of file diff --git a/Homework_5.2/2D/nview-corners b/Homework_5.2/2D/nview-corners new file mode 100644 index 0000000..5955705 --- /dev/null +++ b/Homework_5.2/2D/nview-corners @@ -0,0 +1,575 @@ + 0 0 * + 1 1 * + 2 2 * + 3 3 * + 4 * 0 + 5 4 * + 6 * 1 + 7 * 2 + 8 * 3 + 9 * 4 + 10 * 5 + 11 5 * + 12 * 6 + 13 * 7 + 14 * 8 + 15 * 9 + 16 6 * + 17 * 10 + 18 7 * + 19 8 * + 20 * 11 + 21 * 12 + 22 * 13 + 23 * 14 + 24 9 * + 25 * 15 + 26 10 * + 27 11 * + 28 * 16 + 29 12 * + 30 * 17 + 31 13 * + 32 14 * + 33 15 * + 34 * 18 + 35 * 19 + 36 * 20 + 37 16 * + 38 * 21 + 39 * 22 + 40 * 23 + 41 * 24 + 42 * 25 + 43 17 * + 44 * 26 + 45 * 27 + 46 * 28 + 47 18 * + 48 * 29 + 49 19 * + 50 * 30 + 51 * 31 + 52 * 32 + 53 20 * + 54 21 * + 55 22 * + 56 * 33 + 57 23 * + 58 24 * + 59 * 34 + 60 * 35 + 61 * 36 + 62 25 * + 63 * 37 + 64 26 * + 65 * 38 + 66 27 * + 67 28 * + 68 29 * + 69 30 * + 70 31 * + 71 * 39 + 72 32 * + 73 * 40 + 74 33 * + 75 34 * + 76 * 41 + 77 35 * + 78 36 * + 79 * 42 + 80 * 43 + 81 37 * + 82 * 44 + 83 38 * + 84 * 45 + 85 39 * + 86 * 46 + 87 40 * + 88 * 47 + 89 * 48 + 90 41 * + 91 42 * + 92 43 * + 93 * 49 + 94 44 * + 95 45 * + 96 * 50 + 97 46 * + 98 47 * + 99 * 51 + 100 * 52 + 101 48 * + 102 49 * + 103 * 53 + 104 50 * + 105 51 * + 106 * 54 + 107 52 * + 108 * 55 + 109 * 56 + 110 53 * + 111 * 57 + 112 54 * + 113 55 * + 114 * 58 + 115 * 59 + 116 56 * + 117 57 * + 118 58 * + 119 * 60 + 120 * 61 + 121 * 62 + 122 * 63 + 123 * 64 + 124 59 * + 125 60 * + 126 61 * + 127 62 * + 128 63 * + 129 64 * + 130 65 * + 131 * 65 + 132 * 66 + 133 66 * + 134 * 67 + 135 * 68 + 136 67 * + 137 68 * + 138 69 * + 139 * 69 + 140 70 * + 141 * 70 + 142 71 * + 143 72 * + 144 73 * + 145 74 * + 146 75 * + 147 76 * + 148 77 * + 149 78 * + 150 79 * + 151 * 71 + 152 80 * + 153 * 72 + 154 81 * + 155 82 * + 156 83 * + 157 * 73 + 158 * 74 + 159 84 * + 160 85 * + 161 86 * + 162 87 * + 163 88 * + 164 89 * + 165 90 * + 166 91 * + 167 * 75 + 168 * 76 + 169 92 * + 170 93 * + 171 94 * + 172 95 * + 173 * 77 + 174 96 * + 175 97 * + 176 * 78 + 177 * 79 + 178 98 * + 179 99 * + 180 100 * + 181 101 * + 182 102 * + 183 103 * + 184 104 * + 185 105 * + 186 106 * + 187 107 * + 188 * 80 + 189 108 * + 190 109 * + 191 110 * + 192 * 81 + 193 111 * + 194 * 82 + 195 112 * + 196 * 83 + 197 113 * + 198 114 * + 199 115 * + 200 116 * + 201 * 84 + 202 117 * + 203 118 * + 204 119 * + 205 120 * + 206 121 * + 207 * 85 + 208 122 * + 209 * 86 + 210 * 87 + 211 123 * + 212 * 88 + 213 124 * + 214 125 * + 215 126 * + 216 * 89 + 217 127 * + 218 128 * + 219 129 * + 220 130 * + 221 * 90 + 222 131 * + 223 * 91 + 224 132 * + 225 133 * + 226 134 * + 227 135 * + 228 136 * + 229 * 92 + 230 137 * + 231 138 * + 232 139 * + 233 140 * + 234 141 * + 235 142 * + 236 143 * + 237 144 * + 238 145 * + 239 146 * + 240 147 * + 241 148 * + 242 * 93 + 243 149 * + 244 150 * + 245 151 * + 246 152 * + 247 * 94 + 248 153 * + 249 154 * + 250 * 95 + 251 155 * + 252 156 * + 253 157 * + 254 158 * + 255 159 * + 256 160 * + 257 * 96 + 258 * 97 + 259 161 * + 260 * 98 + 261 162 * + 262 163 * + 263 164 * + 264 * 99 + 265 * 100 + 266 165 * + 267 * 101 + 268 * 102 + 269 166 * + 270 167 * + 271 168 * + 272 169 * + 273 * 103 + 274 170 * + 275 171 * + 276 172 * + 277 173 * + 278 174 * + 279 * 104 + 280 * 105 + 281 * * + 282 175 * + 283 176 * + 284 * 107 + 285 * 108 + 286 177 * + 287 178 * + 288 179 * + 289 180 * + 290 181 * + 291 182 * + 292 183 * + 293 184 * + 294 185 * + 295 * 109 + 296 186 * + 297 * 110 + 298 187 * + 299 188 * + 300 189 * + 301 190 * + 302 * 111 + 303 191 * + 304 192 * + 305 193 * + 306 194 * + 307 * 112 + 308 * 113 + 309 195 * + 310 196 * + 311 197 * + 312 198 * + 313 199 * + 314 200 * + 315 201 * + 316 202 * + 317 203 * + 318 * 114 + 319 204 * + 320 205 * + 321 206 * + 322 207 * + 323 208 * + 324 209 * + 325 210 * + 326 * 115 + 327 211 * + 328 212 * + 329 213 * + 330 214 * + 331 * 116 + 332 215 * + 333 216 * + 334 217 * + 335 218 * + 336 219 * + 337 220 * + 338 221 * + 339 222 * + 340 223 * + 341 * 117 + 342 224 * + 343 * 118 + 344 225 * + 345 226 * + 346 227 * + 347 228 * + 348 229 * + 349 230 * + 350 231 * + 351 232 * + 352 233 * + 353 234 * + 354 235 * + 355 236 * + 356 237 * + 357 238 * + 358 239 * + 359 240 * + 360 241 * + 361 * 119 + 362 242 * + 363 243 * + 364 244 * + 365 * 120 + 366 245 * + 367 * 121 + 368 * 122 + 369 246 * + 370 247 * + 371 248 * + 372 249 * + 373 250 * + 374 * 123 + 375 * 124 + 376 251 * + 377 * 125 + 378 * 126 + 379 252 * + * 253 127 + * 254 128 + * 255 129 + * 256 130 + * 257 131 + * 258 132 + * 259 133 + * 260 134 + * 261 * + * 262 136 + * 263 137 + * 264 138 + * 265 139 + * 266 140 + * 267 141 + * 268 142 + * 269 143 + * 270 144 + * 271 145 + * 272 146 + * 273 147 + * 274 148 + * 275 149 + * 276 150 + * 277 151 + * 278 152 + * 279 153 + * 280 154 + * 281 155 + * 282 156 + * 283 157 + * 284 158 + * 285 159 + 380 286 160 + 381 287 161 + 382 288 162 + 383 289 163 + 384 290 164 + 385 291 165 + * 292 166 + 387 293 167 + 388 294 168 + 389 295 169 + 390 296 170 + 391 297 171 + 392 298 * + 393 299 173 + 394 300 174 + 395 301 175 + 396 302 176 + 397 303 177 + 398 304 178 + 399 305 179 + 400 306 180 + 401 * * + 402 308 182 + 403 309 183 + 404 310 184 + 405 311 185 + 406 * * + 407 313 187 + 408 314 188 + 409 315 189 + 410 316 190 + 411 317 191 + 412 318 192 + * 319 * + 414 320 194 + 415 321 195 + 416 322 196 + 417 323 197 + 418 324 198 + 419 325 199 + 420 326 200 + * * * + 422 328 202 + * 329 * + 424 330 204 + 425 331 205 + 426 332 206 + 427 333 207 + 428 334 208 + 429 335 209 + 430 336 210 + 431 337 211 + 432 338 212 + 433 339 213 + 434 340 214 + 435 341 215 + 436 342 216 + 437 343 217 + * 344 218 + 439 345 219 + 440 346 220 + 441 347 221 + 442 348 222 + 443 349 223 + 444 350 224 + 445 351 225 + 446 352 226 + 447 353 227 + 448 354 228 + 449 355 229 + 450 356 230 + 451 357 231 + 452 358 232 + 453 359 233 + 454 360 234 + 455 361 235 + 456 362 236 + 457 363 237 + 458 364 238 + 459 365 239 + 460 366 240 + 461 367 241 + 462 368 242 + 463 369 243 + 464 370 244 + 465 371 245 + 466 372 246 + 467 373 247 + 468 374 248 + 469 375 249 + 470 376 250 + 471 377 251 + 472 378 * + 473 379 * + 474 380 254 + 475 381 255 + 476 382 256 + 477 383 257 + 478 384 258 + 479 385 259 + 480 386 260 + 481 387 261 + 482 388 262 + 483 389 * + 484 390 264 + 485 391 265 + 486 392 266 + 487 393 267 + 488 394 268 + 489 395 269 + 490 396 270 + 491 397 271 + 492 398 272 + 493 399 273 + 494 400 * + 495 401 275 + 496 402 276 + 497 403 277 + 498 404 278 + 499 405 279 + 500 406 280 + 501 * 281 + 502 408 282 + 503 409 283 + 504 410 284 + 505 411 285 + 506 412 286 + * 413 287 + 508 414 288 + 509 415 289 + 510 416 290 + * 417 291 + 512 418 292 + 513 419 293 + 514 420 294 + 515 421 295 + 516 422 296 + 517 423 297 + 518 424 298 + 519 425 299 + 520 426 300 + 521 427 301 + 522 428 302 + 523 429 303 + 524 430 * + 525 431 305 + 526 432 306 + * 433 307 + 528 434 308 + 529 435 309 + 530 436 310 + * 437 311 + 532 438 312 + * 439 313 + * 440 * + 535 441 * + 536 442 * + * 443 * + 538 444 318 + * 445 319 + 540 446 320 + 541 447 * diff --git a/Homework_5.2/2D/nview-lines b/Homework_5.2/2D/nview-lines new file mode 100644 index 0000000..f076c28 --- /dev/null +++ b/Homework_5.2/2D/nview-lines @@ -0,0 +1,177 @@ + 0 0 0 + 1 1 1 + 2 2 2 + 3 3 3 + 4 4 4 + 5 5 5 + 6 6 6 + 7 7 7 + 8 8 8 + 9 9 9 + 10 10 10 + 11 11 11 + 12 12 12 + 13 13 13 + 14 14 14 + 15 15 15 + 16 16 16 + 17 17 17 + 18 18 18 + 19 19 19 + 20 20 20 + 21 21 21 + 22 22 22 + 23 23 23 + 24 24 24 + 25 25 25 + 26 26 26 + 27 27 27 + 28 28 28 + 29 29 29 + 30 30 30 + 31 31 31 + 32 32 32 + 33 33 33 + 34 34 34 + 35 35 35 + 36 36 36 + 37 37 37 + 38 38 38 + 39 39 39 + 40 40 40 + 41 41 41 + 42 42 42 + 43 43 43 + 44 44 44 + 45 45 45 + 46 46 46 + 47 47 47 + 48 48 48 + 49 49 49 + 50 50 50 + 51 51 51 + 52 52 52 + 53 53 53 + 54 54 54 + 55 55 55 + 56 56 56 + 57 57 57 + 58 58 58 + 59 59 59 + 60 60 60 + 61 61 61 + 62 62 62 + 63 63 63 + 64 64 64 + 65 65 65 + 66 66 66 + 67 67 67 + 68 68 68 + 69 69 69 + 70 70 70 + 71 71 71 + 72 72 72 + 73 73 73 + 74 74 74 + 75 75 75 + 76 76 76 + 77 77 77 + 78 78 78 + 79 79 79 + 80 80 80 + 81 81 81 + 82 82 82 + 83 83 83 + 84 84 84 + 85 85 85 + 86 86 86 + 87 87 87 + 88 88 88 + 89 89 89 + 90 90 90 + 91 91 91 + 92 92 92 + 93 93 93 + 94 94 94 + 95 95 95 + 96 96 96 + 97 97 97 + 98 98 98 + 99 99 99 + 100 100 100 + 101 101 101 + 102 102 102 + 103 103 103 + 104 104 104 + 105 105 105 + 106 106 106 + 107 107 107 + 108 108 108 + 109 109 109 + 110 110 110 + 111 111 111 + 112 112 112 + 113 113 113 + 114 114 114 + 115 115 115 + 116 116 116 + 117 117 117 + 118 118 118 + 119 119 119 + 120 120 120 + 121 121 121 + 122 122 122 + 123 123 123 + 124 124 124 + 125 125 125 + 126 126 126 + 127 127 127 + 128 128 128 + 129 129 129 + 130 130 130 + 131 131 131 + 132 132 132 + 133 133 133 + 134 134 134 + 135 135 135 + 136 136 136 + 137 137 137 + 138 138 138 + 139 139 139 + 140 140 140 + 141 141 141 + 142 142 142 + 143 143 143 + 144 144 144 + 145 145 145 + 146 146 146 + 147 147 147 + 148 148 148 + 149 149 149 + 150 150 150 + 151 151 151 + 152 152 152 + 153 153 153 + 154 154 154 + 155 155 155 + 156 156 156 + 157 157 157 + 158 158 158 + 159 159 159 + 160 160 160 + 161 161 161 + 162 162 162 + 163 163 163 + 164 164 164 + 165 165 165 + 166 166 166 + 167 167 167 + 168 168 168 + 169 169 169 + 170 170 170 + 171 171 171 + 172 172 172 + 173 173 173 + 174 174 174 + 175 175 175 + 176 176 176 diff --git a/Homework_5.2/3D/README-3D b/Homework_5.2/3D/README-3D new file mode 100644 index 0000000..35cda7a --- /dev/null +++ b/Homework_5.2/3D/README-3D @@ -0,0 +1,8 @@ + 3D reconstruction + ----------------- + +Files: + ###.P 3x4 camera projection matrix, one per image. + p3d 3D points. ASCII x y z coordinates, one per line + l3d 3D line segments. ASCII x0 y0 z0 x1 y1 z1 one per line + arec.wrl VRML 1.0 file with points, lines and cameras \ No newline at end of file diff --git a/Homework_5.2/3D/l3d b/Homework_5.2/3D/l3d new file mode 100644 index 0000000..4be8dc1 --- /dev/null +++ b/Homework_5.2/3D/l3d @@ -0,0 +1,177 @@ + 3.7987359e-01 4.3329707e+00 -1.1007211e+00 1.4465859e+00 4.3329707e+00 -1.1007211e+00 + 3.9280047e-01 4.3142323e+00 -3.1585982e+00 1.4631623e+00 4.3142323e+00 -3.1585982e+00 + 3.4808889e+00 9.0877155e-01 3.1793866e-01 4.3926394e+00 9.0877155e-01 3.1793866e-01 + 2.1721912e+00 4.3349486e+00 -1.7906553e-01 6.9948474e-01 4.3349486e+00 -1.7906553e-01 + 4.4699253e+00 2.6026220e+00 -2.6856990e-02 3.4769378e+00 2.6026220e+00 -2.6856990e-02 + 4.6000398e+00 2.3150873e+00 2.2039226e-01 5.3679147e+00 2.3150873e+00 2.2039226e-01 + 5.4898098e+00 2.5780271e+00 -3.9742258e-02 4.5942124e+00 2.5780271e+00 -3.9742258e-02 + 2.1737073e+01 -2.4897941e+01 -1.5633306e+01 2.4845167e+01 -2.4897941e+01 -1.5633306e+01 + 3.4538917e+00 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3.3407139e-02 + 4.3520343e+00 -6.0413290e-01 2.6309313e+00 + 5.3667670e+00 -2.8479408e-01 3.9365875e-02 + 3.1923853e+00 -6.2141059e+00 5.1624334e+00 + 1.4225223e+00 1.0465825e+00 -7.0223162e-02 diff --git a/Homework_5.2/camera.py b/Homework_5.2/camera.py new file mode 100644 index 0000000..1abf519 --- /dev/null +++ b/Homework_5.2/camera.py @@ -0,0 +1,74 @@ +from numpy import * +from scipy import linalg + + +class Camera(object): + """ Class for representing pin-hole cameras. """ + + def __init__(self,P): + """ Initialize P = K[R|t] camera model. """ + self.P = P + self.K = None # calibration matrix + self.R = None # rotation + self.t = None # translation + self.c = None # camera center + + + def project(self,X): + """ Project points in X (4*n array) and normalize coordinates. """ + + x = dot(self.P,X) + for i in range(3): + x[i] /= x[2] + return x + + + def factor(self): + """ Factorize the camera matrix into K,R,t as P = K[R|t]. """ + + # factor first 3*3 part + K,R = linalg.rq(self.P[:,:3]) + + # make diagonal of K positive + T = diag(sign(diag(K))) + if linalg.det(T) < 0: + T[1,1] *= -1 + + self.K = dot(K,T) + self.R = dot(T,R) # T is its own inverse + self.t = dot(linalg.inv(self.K),self.P[:,3]) + + return self.K, self.R, self.t + + + def center(self): + """ Compute and return the camera center. """ + + if self.c is not None: + return self.c + else: + # compute c by factoring + self.factor() + self.c = -dot(self.R.T,self.t) + return self.c + + + +# helper functions + +def rotation_matrix(a): + """ Creates a 3D rotation matrix for rotation + around the axis of the vector a. """ + R = eye(4) + R[:3,:3] = linalg.expm([[0,-a[2],a[1]],[a[2],0,-a[0]],[-a[1],a[0],0]]) + return R + + +def rq(A): + from scipy.linalg import qr + + Q,R = qr(flipud(A).T) + R = flipud(R.T) + Q = Q.T + + return R[:,::-1],Q[::-1,:] diff --git a/Homework_5.2/func_triangulate.py b/Homework_5.2/func_triangulate.py new file mode 100644 index 0000000..a59749c --- /dev/null +++ b/Homework_5.2/func_triangulate.py @@ -0,0 +1,23 @@ +import numpy + +# Compute the least square triangulation of a point pair +def triangulate_point(x1,x2,P1,P2): + + M = numpy.zeros((6,6)) + M[:3,:4] = P1 + M[3:,:4] = P2 + M[:3,4] = -x1 + M[3:,5] = -x2 + + U,S,V = numpy.linalg.svd(M) + X = V[-1,:4] + + return X / X[3] + +# Write triangulation function for two view points in x1, x2 +def triangulate(x1,x2,P1,P2): + + n = x1.shape[1] + + X = [ triangulate_point(x1[:,i],x2[:,i],P1,P2) for i in range(n)] + return numpy.array(X).T \ No newline at end of file diff --git a/Homework_5.2/main_triangulate.py b/Homework_5.2/main_triangulate.py new file mode 100644 index 0000000..c2a8baf --- /dev/null +++ b/Homework_5.2/main_triangulate.py @@ -0,0 +1,41 @@ +import func_triangulate +import numpy +import camera +from PIL import Image + +# Read right, left stereo image +im1 = numpy.array(Image.open('stereo/left.jpg')) +im2 = numpy.array(Image.open('stereo/right.jpg')) + +# Read 2D point in image from already save-file +points2D = [numpy.loadtxt('2D/00'+str(i+1)+'.corners').T for i in range(3)] + +# Read real 3D point from already save-file +points3D = numpy.loadtxt('3D/p3d').T + +# Read corresponding point between two images from already save-file +corr = numpy.genfromtxt('2D/nview-corners',dtype='int',missing='*') + +# Read camera matrix +P = [camera.Camera(numpy.loadtxt('2D/00'+str(i+1)+'.P')) for i in range(3)] + +# index for correspond points in two images +ndx = (corr[:,0]>=0) & (corr[:,1]>=0) + +x1 = points2D[0][:,corr[ndx,0]] +x1 = numpy.vstack( (x1,numpy.ones(x1.shape[1])) ) + +x2 = points2D[1][:,corr[ndx,1]] +x2 = numpy.vstack( (x2,numpy.ones(x2.shape[1])) ) + +# xt is a true 3D point +xt = points3D[:,ndx] +xt = numpy.vstack( (xt,numpy.ones(xt.shape[1])) ) + +# xest is a estimation of 3D point +xest = func_triangulate.triangulate(x1,x2,P[0].P,P[1].P) + +print 'Estimation 3D point' +print xest[:,:3] +print 'True 3D point' +print xt[:,:3] \ No newline at end of file diff --git a/Homework_5.2/stereo/left.jpg b/Homework_5.2/stereo/left.jpg new file mode 100644 index 0000000..1e8a972 Binary files /dev/null and b/Homework_5.2/stereo/left.jpg differ diff --git a/Homework_5.2/stereo/right.jpg b/Homework_5.2/stereo/right.jpg new file mode 100644 index 0000000..9d522ac Binary files /dev/null and b/Homework_5.2/stereo/right.jpg differ